scholarly journals Bond Graph Based Modal Representations And Model Reduction Of Lumped Parameter Systems

2006 ◽  
Author(s):  
L. S. Louca
Keyword(s):  
Model Reduction ◽  
Bond Graph ◽  
Lumped Parameter

Power Conserving Bond Graph Based Modal Representations and Model Reduction of Lumped Parameter Systems

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Loucas S. Louca
Keyword(s):  
Model Reduction ◽  
Linear Systems ◽  
Controller Design ◽  
Physical Space ◽  
Order Reduction ◽  
Bond Graph ◽  
Harmonic Excitation ◽  
Model Complexity ◽  
Modal Decomposition ◽  
Lumped Parameter

Dynamic analysis is extensively used to study the behavior of continuous and lumped parameter linear systems. In addition to the physical space, analyses can also be performed in the modal space where very useful frequency information of the system can be extracted. More specifically, modal analysis can be used for the analysis and controller design of dynamic systems, where reduction of model complexity without degrading its accuracy is often required. The reduction of modal models has been extensively studied and many reduction techniques are available. The majority of these techniques use frequency as the metric to determine the reduced model. This paper describes a new method for calculating modal decompositions of lumped parameter systems with the use of the bond graph formulation. The modal decomposition is developed through a power conserving coordinate transformation. The generated modal decomposition model is then used as the basis for reducing its size and complexity. The model reduction approach is based on the previously developed model order reduction algorithm (MORA), which uses the energy-based activity metric in order to generate a series of reduced models. The activity metric was originally developed for the generic case of nonlinear systems; however, in this work, the activity metric is adapted for the case of linear systems with single harmonic excitation. In this case closed form expressions are derived for the calculation of activity. An example is provided to demonstrate the power conserving transformation, calculation of the modal power and the elimination of unimportant modes or modal elements.

Bond Graph Sign Conventions

1975 ◽  
Vol 97 (2) ◽  
pp. 184-188 ◽  
Author(s):  
A. S. Perelson
Keyword(s):  
Graph Model ◽  
Bond Graph ◽  
Equivalence Classes ◽  
Parameter System ◽  
Bond Graphs ◽  
Lumped Parameter ◽  
Oriented Object

The lack of arbitrariness in the choice of bond graph sign conventions is established. It is shown that an unoriented bond graph may have no unique meaning and that with certain choices of orientation a bond graph may not correspond to any lumped parameter system constructed from the same set of elements. Network interpretations of these two facts are given. Defining a bond graph as an oriented object leads to the consideration of equivalence classes of oriented bond graphs which represent the same system. It is also shown that only changes in the orientation of bonds connecting 0-junctions and 1-junctions can lead to changes in the observable properties of a bond graph model.

A Lumped Parameter Electromechanical Model for Describing the Nonlinear Behavior of Piezoelectric Actuators

1997 ◽  
Vol 119 (3) ◽  
pp. 478-485 ◽  
Author(s):  
M. Goldfarb ◽  
N. Celanovic
Keyword(s):  
System Analysis ◽  
Nonlinear Behavior ◽  
Piezoelectric Actuators ◽  
Bond Graph ◽  
Lumped Parameter Model ◽  
Input Output ◽  
Mechanical Stiffness ◽  
Analysis And Design ◽  
Lumped Parameter ◽  
Proposed Model

A lumped-parameter model of a piezoelectric stack actuator has been developed to describe actuator behavior for purposes of control system analysis and design, and in particular for control applications requiring accurate position tracking performance. In addition to describing the input-output dynamic behavior, the proposed model explains aspects of nonintuitive behavioral phenomena evinced by piezoelectric actuators, such as the input-output rate-independent hysteresis and the change in mechanical stiffness that results from altering electrical load. Bond graph terminology is incorporated to facilitate the energy-based formulation of the actuator model. The authors propose a new bond graph element, the generalized Maxwell resistive capacitor, as a lumped-parameter causal representation of rate-independent hysteresis. Model formulation is validated by comparing results of numerical simulations to experimental data.

On Gyrobondgraphs and Their Uses

1978 ◽  
Vol 100 (1) ◽  
pp. 76-82 ◽  
Author(s):  
R. C. Rosenberg
Keyword(s):  
Bond Graph ◽  
Energy Structure ◽  
Engineering Systems ◽  
Graph Models ◽  
Point Of Interest ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Five Elements ◽  
System Equations ◽  
Recent Arrival

Graphical representations of lumped-parameter models for physical and engineering systems have been in use for some time. A relatively recent arrival is the bond graph, which displays energy flow and energy structure explicitly. Bond graphs are finding increasing use in a variety of applications, including classical electromechanical, hydraulic, and thermal energy systems as well as chemical and biological processes. In addition, there has been some effort to extend the approach to energy-like macroeconomic systems. The standard bond graph approach uses the same basic elements commonly found in network theory, although the graphing scheme is different. This paper defines a specific type of bond graph—the gyrobondgraph—and shows how it serves as a canonical form for a large class of lumped-parameter multiport models. The gyrobondgraph is based on only five elements and a standard graph format. A transformation procedure is described for obtaining a gyrobondgraph from a standard bond graph. The formulation of system equations associated with a gyrobondgraph is discussed briefly, and, as a point of interest, Tellegen’s Theorem in quasi-power form is derived. The gyrobondgraph appears to be an important new tool for the exploration of multiport system theory; furthermore, it is a source of new techniques for the computer simulation of bond graph models.

Energy-Based Bond Graph Model Reduction

2011 ◽  
pp. 53-103
Author(s):  
L.S. Louca ◽  
D.G. Rideout ◽  
T. Ersal ◽  
J.L. Stein
Keyword(s):  
Model Reduction ◽  
Graph Model ◽  
Bond Graph

Linear, lumped parameter transformer model reduction technique

1995 ◽  
Vol 10 (2) ◽  
pp. 853-861 ◽  
Author(s):  
M. Gutierrez ◽  
R.C. Degeneff ◽  
P.J. McKenny ◽  
J.M. Schneider
Keyword(s):  
Model Reduction ◽  
Reduction Technique ◽  
Lumped Parameter ◽  
Transformer Model ◽  
Model Reduction Technique

Bond Graph Models for Fluid Dynamic Systems

1972 ◽  
Vol 94 (3) ◽  
pp. 222-229 ◽  
Author(s):  
D. Karnopp
Keyword(s):  
Fluid Dynamic ◽  
Nonlinear Behavior ◽  
Bond Graph ◽  
Distributed Parameter ◽  
Graph Models ◽  
Modeling Process ◽  
Fluid Systems ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Control Volumes

The modeling process whereby distributed parameter fluid systems are described approximately by lumped parameter models is discussed using bond graph techniques. It is shown that despite the analogies which exist between some fluid systems and other physical systems, the lumping process for fluid systems introduces forms of nonlinear behavior not often encountered in other types of systems. Many such effects may be traced to the desire to use control volumes and Eulerian rather than Lagrangian descriptions of the fluid systems.

A Dynamic Model of a Concentric LADD Actuator

1983 ◽  
Vol 105 (3) ◽  
pp. 157-164 ◽  
Author(s):  
K. L. Pottebaum ◽  
J. J. Beaman
Keyword(s):  
Dynamic Model ◽  
Rotational Motion ◽  
Dynamic Models ◽  
Translational Motion ◽  
Bond Graph ◽  
Second Order ◽  
Sixth Order ◽  
Order Model ◽  
Lumped Parameter ◽  
Elasticity Effects

A LADD actuator is a device capable of converting rotational motion to translational motion and has potential for use in manipulators, robotics, and prosthetics. Two low order lumped parameter dynamic models of a concentric LADD actuator have been formulated and experimentally verified. The sixth order model includes elasticity effects while the second order model does not. Both of these models are presented in bond graph terminology in order to ease their use in overall system models.

scholarly journals Bond Graph Model of Cerebral Circulation: Toward Clinically Feasible Systemic Blood Flow Simulations

2020 ◽  
Author(s):  
Shan Su ◽  
Pablo J. Blanco ◽  
Lucas O. Müller ◽  
Peter J. Hunter ◽  
Soroush Safaei
Keyword(s):  
Cerebral Circulation ◽  
Graph Model ◽  
Bond Graph ◽  
The Body ◽  
Lumped Parameter Model ◽  
Desktop Computer ◽  
Detailed Model ◽  
Simulation Speed ◽  
Lumped Parameter ◽  
Proposed Model

The primary paper Safaei et al. (2018) proposed an anatomically detailed model of the human cerebral circulation that runs faster than real-time on a desktop computer and is designed for use in clinical settings when the speed of response is important. Based on a one-dimensional formulation of the flow of an incompressible fluid in distensible vessels, a lumped parameter model was developed for 218 arterial segments. The proposed model improved simulation speed by approximately 200-fold while preserved accuracy. Bond graph formulation was used to ensure mass and energy conservation. The model predicted the pressure and flow signatures in the body.

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